1. ## About characteristic of rings

What can be said about the characteristic of a ring R in which x=-x for each x in R?

Thank You

2. ## i picked up some alien signals

Originally Posted by hercules
What can be said about the characteristic of a ring R in which x=-x for each x in R?
Thank You
I think i got it now. But if anyone has any ideas and suggestions...please do post them ....they will help me understand better.

3. Originally Posted by hercules
What can be said about the characteristic of a ring R in which x=-x for each x in R?

Thank You
The charachteristic is 2. Because if $\displaystyle x=-x\implies x + x = 0$ in particular $\displaystyle 2\cdot 1 = 0$.

4. Originally Posted by ThePerfectHacker
The charachteristic is 2. Because if $\displaystyle x=-x\implies x + x = 0$ in particular $\displaystyle 2\cdot 1 = 0$.
Why did you pick 1 for x value specifically? (where 2x=0)

5. Originally Posted by hercules
Why did you pick 1 for x value specifically? (where 2x=0)
It really works for any value of x. But field charachteristics are defined for 1. Because if 1 + 1 = 0 then it is true for any element. That is why we resrict out attention to 1.

6. Originally Posted by hercules
Why did you pick 1 for x value specifically? (where 2x=0)
TPH is right. To supplement his comments, read the paragraph right under the definition of the characteristic in your text

7. Originally Posted by Jhevon
TPH is right. To supplement his comments, read the paragraph right under the definition of the characteristic in your text

Isn't that only if ring has unity?

Don't worry about it ...it just takes me longer to get it but i'll get it.

8. Originally Posted by hercules
Isn't that only if ring has unity?

Don't worry about it ...it just takes me longer to get it but i'll get it.
1 is the unity element. otherwise, we have 2x = 0 for all x in R, so either definition is satisfied. I was just trying to show you why considering 1 was relevant

9. Originally Posted by hercules
Isn't that only if ring has unity?
I believe field characheristics are only defined for commutative unitary rings.